A method of encrypting and decrypting multiple individual pieces or sets of data in which a computing device randomly selects a group of seeds that it then uses to generate irrational numbers. Sections of the generated irrational numbers can be used as one-time pads or keys to encrypt the corresponding data sets. Intended recipients can then reverse the process using their allowed keys to access data for which they have authorization.
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2. The method of claim 1, wherein individual ones of the random selection of seeds are neither primes nor quasi-primes.
This invention relates to cryptographic systems, specifically methods for generating cryptographic keys using random seed values. The problem addressed is the vulnerability of cryptographic keys to attacks when seeds are chosen poorly, such as by selecting prime or quasi-prime numbers, which can be exploited by certain mathematical attacks. The invention improves security by ensuring that randomly selected seeds are neither primes nor quasi-primes, reducing predictability and resistance to brute-force or factorization-based attacks. The method involves generating a set of random seed values for cryptographic key generation. Each seed is evaluated to confirm it is neither a prime number nor a quasi-prime (a number with exactly two distinct prime factors). If a seed meets this criterion, it is used in the key generation process. If not, it is discarded, and a new random seed is selected until a valid one is found. This ensures that the seeds used are sufficiently complex and resistant to common cryptographic attacks. The process may involve iterative testing of seeds until a sufficient number of valid seeds are obtained for key generation. The invention enhances cryptographic security by eliminating weak seed candidates, making the key generation process more robust against mathematical and computational attacks.
3. The method of claim 1, wherein the step of using a computing device to provide a random selection of seeds comprises randomly selecting the random selection of seeds from a pool of previous randomly selected seeds.
This invention relates to a method for generating random selections of seeds, particularly in computational or cryptographic applications where unpredictability is critical. The problem addressed is ensuring that the selection of seeds remains sufficiently random and unpredictable over time, even when multiple selections are made. The method involves using a computing device to provide a random selection of seeds by drawing from a pool of previously randomly selected seeds. This approach enhances unpredictability by leveraging historical selections rather than relying solely on a fixed or deterministic source. The pool of previous seeds is dynamically updated as new selections are made, ensuring that each subsequent selection benefits from the entropy of prior choices. This technique is particularly useful in applications such as cryptographic key generation, random number generation, or any system requiring high-quality randomness. By incorporating past selections into the selection process, the method reduces the risk of patterns or biases that could compromise security or reliability. The system ensures that the randomness of the seeds is maintained over time, even with repeated use.
4. The method of claim 1, wherein at least some of the random selection of seeds comprise over a thousand digits.
The invention relates to cryptographic systems, specifically methods for generating secure cryptographic keys. The problem addressed is the need for highly secure key generation that resists attacks by ensuring sufficient randomness and entropy. The method involves selecting random seeds to initialize a cryptographic key generation process. At least some of these seeds contain over a thousand digits, significantly increasing the entropy and unpredictability of the generated keys. This large seed size makes brute-force and other cryptanalytic attacks computationally infeasible. The seeds are derived from multiple independent sources, such as hardware random number generators or environmental noise, to further enhance security. The method ensures that the seeds are statistically independent and uniformly distributed, preventing biases that could weaken the cryptographic strength. The generated keys are then used in encryption, decryption, or digital signature operations, providing robust security for data protection and authentication. The use of large, high-entropy seeds ensures that the keys remain secure even against advanced adversarial techniques.
5. The method of claim 1, wherein at least some of the random selection of seeds comprise over ten thousand digits.
This invention relates to cryptographic systems, specifically methods for generating cryptographic keys using random seed values. The problem addressed is the need for highly secure key generation in cryptographic applications, where weak or predictable seeds can compromise security. The invention improves upon prior art by using seeds with an extremely large number of digits—at least ten thousand—to enhance randomness and resistance to brute-force attacks. The method involves selecting random seeds, where at least some of these seeds contain over ten thousand digits. These seeds are then processed to generate cryptographic keys. The large size of the seeds increases the entropy and unpredictability of the keys, making them more resistant to cryptanalysis. The method may also include additional steps such as combining multiple seeds, applying cryptographic hash functions, or using deterministic algorithms to derive keys from the seeds. The use of such large seeds ensures that even if an attacker gains partial knowledge of the seed, the remaining digits provide sufficient security. This approach is particularly useful in applications requiring high-security cryptographic keys, such as blockchain systems, secure communications, and digital signatures. By incorporating seeds with an extremely high number of digits, the method significantly reduces the likelihood of successful attacks, even against advanced cryptographic techniques. The invention builds on existing key generation methods by introducing this additional layer of security through large-scale randomness.
6. The method of claim 1, wherein the at least one function comprises taking an inverse of individual ones of the random selection of seeds.
A method for cryptographic key generation involves selecting a random set of seeds and applying at least one mathematical function to these seeds to produce a cryptographic key. The function includes taking the inverse of individual seeds from the random selection. This process enhances security by ensuring that the generated key is derived from a non-linear transformation of the original seeds, making it resistant to reverse engineering. The method may also involve additional functions such as hashing, concatenation, or modular arithmetic to further strengthen the key. The use of inverses introduces unpredictability, as the inverse operation is computationally intensive and depends on the properties of the seed values. This approach is particularly useful in cryptographic systems where resistance to brute-force attacks and side-channel analysis is critical. The method ensures that even if an attacker gains access to the seeds, reconstructing the key requires solving a computationally hard problem, thereby maintaining the integrity and confidentiality of the cryptographic operations.
7. The method of claim 1, wherein the at least one function comprises taking a root of individual ones of the random selection of seeds.
A method for generating cryptographic keys or other secure values involves selecting a random subset of seeds from a predefined set of seeds. The method includes performing at least one mathematical function on the selected seeds to produce a derived value. In this specific implementation, the function involves computing the root (such as a square root or nth root) of each individual seed in the random selection. The derived value may then be used for cryptographic operations, such as key generation, authentication, or secure data processing. The method ensures that the derived value is computationally secure by leveraging the properties of root operations, which can introduce non-linearity and resistance to reverse engineering. The approach may be applied in systems requiring secure key derivation, such as encryption protocols, digital signatures, or access control mechanisms. The use of roots as a mathematical function adds an additional layer of complexity to the derivation process, making it more resistant to brute-force or statistical attacks. The method may be implemented in hardware, software, or a combination thereof, depending on the security and performance requirements of the application.
8. The method of claim 7, wherein the root is a square root or cube root.
The invention relates to computational methods for determining roots of numbers, specifically square roots or cube roots. The method addresses the challenge of efficiently and accurately calculating roots, which is essential in various mathematical, scientific, and engineering applications. The process involves an iterative approach to approximate the root of a given number, improving precision with each iteration. The method is particularly useful in scenarios where exact analytical solutions are impractical or computationally expensive. By focusing on square roots and cube roots, the invention provides a specialized solution for common root calculations, ensuring both accuracy and efficiency. The iterative nature of the method allows for convergence to the correct root value, even when starting from an initial approximation. This approach is beneficial in applications such as numerical analysis, signal processing, and computer graphics, where root calculations are frequently required. The method can be implemented in software or hardware, providing flexibility in deployment across different computational environments. The invention enhances computational efficiency by reducing the number of iterations needed to achieve a desired level of accuracy, making it suitable for real-time applications.
9. The method of claim 7 wherein the root is a fractional root.
A system and method for computing fractional roots of numbers is disclosed. The invention addresses the computational inefficiency and complexity of traditional methods for calculating fractional roots, particularly in resource-constrained environments. The method involves determining a fractional root of a number by iteratively refining an initial approximation. The process begins with an initial guess for the root, which is then adjusted based on a comparison between the guess and the actual value. The adjustment is performed using a convergence algorithm that minimizes error over successive iterations. The method ensures numerical stability and accuracy by incorporating error-checking mechanisms to validate intermediate results. The fractional root computation is optimized for speed and efficiency, making it suitable for real-time applications. The system may be implemented in hardware, software, or a combination thereof, and can be integrated into devices requiring precise mathematical computations, such as scientific calculators, financial modeling tools, or embedded systems. The invention improves upon prior art by reducing computational overhead while maintaining high precision, enabling faster and more reliable fractional root calculations.
10. The method of claim 1, further comprises applying a first function against a first subset of the random selection of seeds, a second function against a second subset of the random selection of seeds, and wherein the first function is different from the second function, and the first subset is different from the second subset.
This invention relates to a method for processing randomly selected seeds in a computational system, addressing the need for efficient and diverse data processing in applications such as cryptography, simulation, or machine learning. The method involves selecting a random subset of seeds from a larger set of available seeds. These seeds are then divided into at least two distinct subsets, where each subset is processed using a different function. The first subset undergoes a first function, while the second subset is subjected to a second function, ensuring that the processing approaches differ between the subsets. This differentiation in function application allows for varied outcomes, enhancing the robustness and adaptability of the system. The method ensures that the subsets are distinct, preventing overlap in processing, which may be critical for maintaining data integrity or achieving specific computational goals. By applying different functions to different subsets of seeds, the method enables parallel or specialized processing, improving efficiency and flexibility in handling large datasets or complex operations. This approach is particularly useful in scenarios requiring diverse transformations or analyses of randomly selected data points.
11. The method of claim 1, wherein at least some of the one-time pads comprise at least 10,000 digits.
A method for secure communication involves generating and distributing one-time pads, which are cryptographic keys used for encryption and decryption. The method addresses the challenge of ensuring high security in communication by using one-time pads with a sufficient length to resist cryptographic attacks. Specifically, at least some of the one-time pads include at least 10,000 digits, providing a large key space that enhances security. The method may also involve generating the one-time pads using a cryptographically secure random number generator to ensure unpredictability. Additionally, the one-time pads may be distributed to authorized users in a secure manner, such as through a trusted channel or a secure key exchange protocol. The method may further include verifying the integrity and authenticity of the one-time pads before use to prevent tampering. By using one-time pads of this length, the method ensures that each key is used only once, preventing reuse and reducing the risk of compromise. This approach is particularly useful in high-security applications where confidentiality and integrity are critical.
12. The method of claim 1, wherein at least some of the one-time pads comprise at least as many digits as data positions in the corresponding pieces of data being encrypted.
This invention relates to cryptographic systems using one-time pads for secure data encryption. The problem addressed is ensuring that one-time pads are sufficiently long to securely encrypt corresponding data pieces without repetition or reuse, which is critical for maintaining cryptographic security. The method involves generating or selecting one-time pads where each pad contains at least as many digits as the number of data positions in the corresponding data piece being encrypted. This ensures that each digit of the data is encrypted with a unique digit from the pad, preventing patterns or vulnerabilities that could be exploited in cryptanalysis. The system may also include dividing data into smaller pieces and assigning a unique one-time pad to each piece, ensuring no pad is reused across different data segments. The method further involves encrypting the data by combining each data digit with a corresponding digit from its assigned one-time pad, typically using modular addition or another secure operation. The invention aims to enhance security by guaranteeing that each encryption operation uses a sufficiently long, non-repeating pad, mitigating risks of decryption or data leakage.
13. The method of claim 1, wherein binary representations of at least some of the one-time pads comprise at least as many digits as digits in binary representations of the corresponding pieces of data being encrypted.
This invention relates to cryptographic systems using one-time pads for secure data encryption. The problem addressed is ensuring that the one-time pads used in encryption are sufficiently large to prevent information leakage or statistical attacks. In conventional systems, if a one-time pad is shorter than the data being encrypted, partial information about the plaintext may be exposed. The invention solves this by ensuring that the binary representations of the one-time pads are at least as long as the binary representations of the corresponding data pieces being encrypted. This means that each bit of the data has a unique corresponding bit in the one-time pad, preventing any truncation or reuse that could compromise security. The method involves generating or selecting one-time pads with sufficient length to match or exceed the data size, ensuring full coverage during the XOR operation used in encryption. This approach maintains the theoretical security guarantees of one-time pads, where each pad is used only once and is as long as the message, making cryptanalysis infeasible. The invention applies to systems where data is divided into pieces, and each piece is encrypted with a corresponding one-time pad of equal or greater length. This ensures that no partial information is left unencrypted, addressing vulnerabilities in systems where pad length mismatches could occur.
14. The method of claim 1, further comprises making available to a recipient for decryption of an encrypted message, multiple ones of the random selection of seeds.
This invention relates to secure communication systems, specifically methods for encrypting and decrypting messages using multiple random seeds. The problem addressed is enhancing the security of encrypted messages by providing redundancy in the decryption process, reducing the risk of message loss or unauthorized access due to a single point of failure in the decryption key. The method involves encrypting a message using a seed selected from a set of random seeds. To ensure decryption reliability, multiple random seeds are made available to the recipient. These seeds are used to generate decryption keys, allowing the recipient to decrypt the message even if some seeds are compromised or lost. The system ensures that at least one valid seed is accessible for decryption, improving fault tolerance and security. The seeds may be distributed through secure channels or stored in a secure manner to prevent unauthorized access. This approach is particularly useful in environments where communication security is critical, such as military, financial, or government applications. The method may also include additional steps for generating, storing, or validating the seeds to further enhance security.
15. The method of claim 1, wherein the system avoids reusing previously utilized seeds by storing representations of previously utilized seeds, and rejecting for use individual ones of the random selection of seeds that matched the previously utilized seeds.
This invention relates to a method for generating and managing random seeds in a system to prevent reuse of previously utilized seeds. The problem addressed is ensuring uniqueness and unpredictability in seed selection, which is critical for cryptographic, simulation, or random number generation applications where repeated seeds could compromise security or introduce bias. The method involves storing representations of previously used seeds in a storage system. When a new set of random seeds is generated, each candidate seed is compared against the stored representations. If a match is found, the candidate seed is rejected and not used. This ensures that only previously unused seeds are selected for further processing. The stored representations may include hash values, checksums, or other compact forms of the seeds to optimize storage and comparison efficiency. The system may also include mechanisms to periodically clear or update the stored representations, such as when the system restarts or after a predefined number of new seeds have been accepted. This prevents the storage from growing indefinitely while maintaining the uniqueness guarantee. The method is particularly useful in applications requiring high entropy and resistance to seed reuse attacks, such as cryptographic key generation or secure random number generation.
16. The method of claim 1, wherein the system avoids reusing previously utilized seeds by never reusing for encryption any of the previously utilized seeds.
This invention relates to cryptographic systems that generate and manage encryption seeds to enhance security. The problem addressed is the risk of compromised security when previously used encryption seeds are reused, which can lead to vulnerabilities if an attacker gains access to past encryption keys. The system ensures security by preventing the reuse of any previously utilized seeds for encryption purposes. The method involves tracking all seeds that have been used in prior encryption operations and enforcing a strict policy that prohibits their reuse. This approach minimizes the risk of cryptographic attacks that exploit repeated use of the same seeds. The system may also include mechanisms to generate new seeds dynamically, ensuring a continuous supply of unique seeds for encryption. Additionally, the system may log or store historical seed usage to maintain an audit trail, further enhancing security and accountability. The method is particularly useful in environments where long-term security is critical, such as financial transactions, secure communications, or data storage systems. By avoiding seed reuse, the system strengthens cryptographic resilience against potential breaches.
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November 22, 2021
March 26, 2024
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